Background: The study of non-Newtonian fluids in thin channels is crucial for advancing technologies in microfluidic systems and targeted industrial coating processes. Nanofluids, which exhibit enhanced thermal properties, are of particular interest. This paper investigates the complex flow and heat transfer characteristics of a Sutterby nanofluid (SNF) within a thin channel, considering the combined effects of magnetohydrodynamics (MHD), Brownian motion, and bioconvection of microorganisms. Analyzing such systems is essential for optimizing design and performance in relevant engineering applications. Method: The governing non-linear partial differential equations (PDEs) for the flow, heat, concentration, and bioconvection are derived. Using lubrication theory and appropriate dimensionless variables, this system of PDEs is simplified into a more simplified system of ordinary differential equations (ODEs). The resulting nonlinear ODEs are solved numerically using the boundary value problem (BVP) Midrich method in Maple software to ensure accuracy. Furthermore, data for the Nusselt number, extracted from the numerical solutions, are used to train an artificial neural network (ANN) model based on the Levenberg–Marquardt algorithm. The performance and predictive capability of this ANN model are rigorously evaluated to confirm its robustness for capturing the system’s non-linear behavior. Results: The numerical solutions are analyzed to understand the variations in velocity, temperature, concentration, and microorganism profiles under the influence of various physical parameters. The results demonstrate that the non-Newtonian rheology of the Sutterby nanofluid is significantly influenced by Brownian motion, thermophoresis, bioconvection parameters, and magnetic field effects. The developed ANN model demonstrates strong predictive capability for the Nusselt number, validating its use for this complex system. These findings provide valuable insights for the design and optimization of microfluidic devices and specialized coating applications in industrial engineering.

In the current investigation, we propose the analytical and numerical solutions of the Navier–Stokes equation for the reverse roll coating process (RRCP) using a bath of the Sisko fluid model (SFM). A suitable transformation is applied to the partial differential equation-based mathematical model of SFM-RRCP, resulting in a set of nonlinear ordinary differential equations. The perturbation method has been employed to find the analytical solutions for velocity, flow rate, pressure gradient, pressure, and temperature distribution. The Newton–Raphson method has been used to find coating thickness. Furthermore, numerical integration has been applied to compute some mechanical quantities of interest, including power input and roll separation force. Sensitivity analysis is another approach implemented using response surface methods to examine the impacts of velocity ratio and non-Newtonian parameters on coating thickness, power input, and roll separating forces. The residual graphs and contour diagrams are also shown. It has been observed that as the value of non-Newtonian fluid parameters increases, the velocity profile decreases. However, the coating thickness on the web is a decreasing function. Further, it has been observed that separation points moved toward the nip region when the value of the velocity ratio was raised. Moreover, the sensitivity of roll separating forces and power input to input parameters is negative.